This invention relates generally to impedance matching networks, for matching a source impedance with a load impedance, and, more particularly, to impedance matching networks in which network values are dynamically adjusted to converge on a solution initially, when the load impedance is unknown, and later, as the load impedance changes. A common goal in connecting a source of electrical power to an electrical load is to maximize the power transfer from the source to the load. This goal is met when the output impedance of the source, or generator, is equal to the complex conjugate of the input impedance of the load.
By way of brief background, in alternating current (ac) circuits, impedance has a resistive component, referred to as the real component, and an inductive or capacitive component, referred to as the imaginary component. In conventional complex number notation, an impedance Z is given by Z=R+jX, where R is the real component, X is the imaginary component, and j is an operator equal to the square root of minus one. Impedances are said to be complex conjugates when their resistive components are equal and their imaginary components are equal in magnitude but opposite in sign. If a generator impedance is Z.sub.G =R.sub.G +jX.sub.G, then maximum power will be transferred to a load when the load impedance is Z.sub.L =R.sub.G -jX.sub.G. Another way of thinking of complex conjugates is in terms of vector quantities. A simple resistive impedance may be thought of as a vector with a phase angle of zero. A complex impedance has a magnitude and a phase angle. Impedances that are complex conjugates of each other have equal magnitudes, but phase angles of equal magnitude and opposite sign.
In many circuit applications, the source or generator impedance does not match the load impedance, and an impedance matching network may be connected between the source and the load. Basically, the function of the impedance matching network is to present to the generator an impedance equal to the complex conjugate of the generator impedance, and to present to the load an impedance equal to the complex conjugate of the load impedance. The matching network contains a number of interconnected inductors and capacitors, some of which are adjustable in value to achieve the desired result. Some forms of impedance matching networks operate on the assumption that the magnitude of the network input impedance can be varied by adjusting a particular network value, and that the phase angle of the network input impedance can be independently varied by adjusting another network value. Unfortunately, the assumption is not always correct, even over a narrow range of adjustment, and such a network may easily converge on a false solution, in which either the magnitude or the phase angle may be appropriately matched, but not both.
U.S. Pat. No. 4,951,009 issued in the names of Collins et al., entitled "Tuning Method and Control System for Automatic Matching Network," discloses and claims an improved technique for controlling an impedance matching network. Two variable impedances are cyclically varied, or "dithered," about steady-state values, and the effect of the dithered impedance values on the power reflected from the matching network is observed. The steady-state values of the impedances are continually adjusted to minimize the reflected power, which is indicative of the degree of impedance matching achieved. Dithering the network values allows the determination of partial derivatives, i.e. the rates of change of the reflected power with respect to each network value. Each network value can then be varied until both partial derivatives are practically zero. Although this approach works satisfactorily over a narrow range, it is also susceptible to converging on a false local minimum solution in the characteristic surface relating the reflected power to the variable network values. Although the characteristic may be approximately a paraboloid in shape, with a definite minimum value at which the partial derivatives in both directions are zero, there may be false solutions at which the partial derivatives are zero but a true absolute minimum reflected power has not been achieved.
It will be appreciated from the foregoing that there is still a need for improvement in the field of dynamically adjustable impedance matching networks. The need is particularly acute in the field of plasma processing, as used in the fabrication of semiconductor circuitry. When the electrical load is a plasma, the load impedance is dynamic and nonlinear, and changes as more power is coupled to it, and as other variables, such as gas pressure and composition, are changed. Therefore, although the load impedance may be measured or estimated, for purposes of adjusting a matching network to optimize power transfer, the load impedance will change whenever the network values are adjusted. Accordingly, a dynamically adjustable network is essential for efficiently coupling power to a plasma. The present invention provides an elegant solution to the problems outlined above, as summarized below.